Fitting Nuclear and Magnetic Scattering in GSAS with aPmmm Nuclear Phase and a Fmm'm' Magnetic Phase

In this example,
one crystallographic phase will be modeled with the observed
crystallographic symmetry (Pmmm) and that phase will be used to
compute the nuclear scattering only.
Later,
the full color space group symmetry will be used in a second phase
that will be used for magnetic scattering computation only.
Only the atoms that scatter magnetically (Fe1 and Fe2) need to be included
in this phase.
Some constraints will be required in this example to keep atomic positions and
lattice constants comparable between these phases.

Input model for Nuclear Scattering Phase

The first step in the refinement is to start a new refinement by creating a
new experiment file. Start EXPGUI and enter a new file name
(screen image)
then click on the "Create" button to then create a new, empty, experiment file
(screen image)
and enter a title.

The first step in creating an GSAS refinement is to create a phase. This can
be done from this information:

Go to the Phase panel
(screen image)
and press the "Add Phase" button. To input the information from the CIF,
click on the "PowderCell .CEL file" menu button to bring up a menu of choices
(screen image)
and select "Crystallographic Information File (CIF)"
which brings up a window where the file YBaFeO_Pmmm.cif can be selected.
(screen image);
click on "Open" after the file is
selected.
Click on "Continue" on the add new phase
(screen image)
and on the Check symmetry windows
(screen image)
and then "Add Atoms" on the Adding atoms... window
(screen image)
and the phase has been added, just like that.
Finally, make sure the "Refine Cell" option is not selected,
(screen image)
so that the unit cell parameters
will be refined until later, after the background and scale factor
are first brought into the right range.

Input Diffraction Data

The second step in almost every GSAS refinement is to input diffraction data
(or select data parameters in a simulation). This is done from the Histogram
panel
(screen image).
Click on the "Add New Histogram" button
which brings up the add new histogram window
(screen image).
Press the Select file to select the appropriate GSAS data file
in the Open window
(screen image);
press the open button
and the file names for the both the data file and the instrument parameter files
are loaded (you might see messages about file conversions if the download
process has stripped non-printing characters needed from the files.). Finally,
change the data range to utilize a maximum two-theta of 152 degrees
on the add new histogram window, which
eliminates the last very wide peak from use in the refinement (the fit
would also progress well were this peak included)
(screen image).
Press "Add" on this window and the
diffraction data are now included in the refinement
Finally, change the background function to type 1 with 6 terms by pressing the
"Edit Background" button (this is the authors' preference -- but other
settings could be selected.)
(screen image).
Finally, confirm that the "Refine background" option is selected so that
the background will be fit
(screen image).

Start Initial Fit of Experimental Parameters

The fit can now be started, by pressing the "powpref"
(screen image)
and "genles" buttons
(screen image).
Note that pressing each button starts a program in another
window and then (unless the default settings have been changed) after
each run has been completed, the extra window is closed and the "Load
New" button is pressed on the Reload screen
(screen image).
Note that after the two cycles
of refinement, the chi2 value drops to approximately 44.

At this point the unit cell is refined, by selecting the
the "Refine Cell" option on the Phase panel
(screen image).
Press the "genles" button and
note that the fit improves to a chi2 value of approximately 30
(screen image).
The two-theta zero is now refined
using the "Refine zero" control on the Histogram panel
(screen image).
Press the "genles" button and
note that the fit improves to a chi2 value of approximately 28
(screen image).

Start Initial Fit of Structural Parameters

At this point an initial fit of the structure is performed (although some
researchers might delay this until the magnetic modeling is included). While
under normal conditions, it would be wise to add refinement of variables
over the course of several refinement runs, in this case the model is
quite stable with respect to refinement and this can
be done in a single run. Before starting the refinement, however,
Uiso values for like element
types are grouped together to reduce the number of parameters.
This is done with the Constraints panel
(screen image).
To set up the constraint on the Fe atoms,
Press on the "New Constraints" button, then select them by dragging over
them with the mouse and select UISO in the Variable menu button
(screen image)
and press "Save".
Repeat this with the O atoms,
Press on the "New Constraints" buttton by dragging over those atoms
with the mouse; then select UISO in the Variable menu button
(screen image)
and press "Save".
The Constraints panel will then list the two constraints
(screen image).

To refine the nuclear model, select all atoms on the phase panel
(the right mouse button will do this) and click on the X and U "Refinement
Flag" buttons
(screen image)
so that all atom positions can be optimized in addition to
4 Uiso values (1 for the Fe atoms, 1 for the O atoms, 1 for the Y atom
and 1 for the Ba atom).
Note that the atom positions will only be optimized as far as allowed
by symmetry, so the Ba position at (1/2,1/2,1/2) will not actually change.
Then set the F (fractional occupancy) flag for O8 and O9 only
(screen image).
Press the "genles" button and
note that the fit improves to a chi2 value of approximately 21
(screen image).
A view of the fit in LIVEPLOT shows
the profile terms need some refinement (which will be done later) and there
is significant missing intensity for several low angle reflections
(screen image)
-- not surprising, since magnetic
scattering is not included.

Save work under new name

Before going any further, lets save the project under a new name, so that
it is easy to compare later work to the non-magnetic model, or so that it is
easy to go back to this point to proceed with an alternate magnetic model.
To do this, use the "Save As" option in the EXPGUI "File" menu item.
This opens an experiment file window, where the new name to be used
is specified
(screen image).
The name PmmmFmmm was selected here, since the nuclear structure will be
modeled in space group Pmmm and the magnetic structure in
Fmmm and a new experiment file, named PMMMFMMM.EXP is created.

Input Magnetic Phase

At this time, EXPGUI does not implement many of the controls needed for
magnetic structure fitting. Nonetheless, as will be shown here. it is still
possible to use EXPGUI for many steps, and then use EXPEDT for steps that
cannot be done at present in EXPGUI. This exercise might
also help build appreciation for EXPGUI.

To add a separate magnetic phase, the phase will be added as a standard
(nuclear scattering-only) phase using EXPGUI, then EXPEDT is used
to change a flag so that it contribributes only as a magnetic scatterer.
Also, constraints on atomic, unit cell and profile parameters are needed.
Some of these values can be set from EXPGUI, but others must be set from
EXPEDT.

Note that in the above an (etc.) refers to the a dimension of
the primitive, nuclear cell and z is the coordinate of the second Fe atom.
Thus, before starting, make note of the unit cell parameters (a,
b & c) in the initial nuclear phase as well as the z
coordinate of the second Fe atom and its Uiso value.
(screen image).

As before, to save time, the basic phase information can be read from a CIF,
FeOnly_Fmmm.cif
in file
YBAFEO.zip,
though in this case some editing of the input information will be needed.

First, the phase is loaded by clicking on the "Add Phase" button on the
Phase panel. To input the information from the CIF,
click on the "PowderCell .CEL file" menu button to bring up a menu of choices
and select "Crystallographic Information File (CIF)"
which brings up a window where the file FeOnly_Fmmm.cif can be selected.
(screen image);
click on "Open" after the file is
selected.

In the add new phase window,
change the a, b & c parameters to be twice those of the
first phase, then click on "Continue" on the add new phase
(screen image).
Also, press "Continue" on the Check symmetry window
(screen image).
This causes the Adding atoms... window to be displayed.
(screen image).
In this window, change the z coordinate for atoms Fe2a and Fe2b based
on the z coordinate of the second Fe atom. Also change the Uiso value
ot agree with the Uiso values for the atoms in phase 1
(screen image)
Finally, press the "Add Atoms" button on this window
to add the phase.

Setup Magnetic Phase

To change the flag for the second phase, the EXPEDT program is used.
This can be invoked from EXPGUI, by pressing the EXPEDT button or from the
Powder and Xtal menus. In EXPEDT, use the following commands:

Y

P

P

m 2

c

x x x x

where command 1) [Y] indicates the correct file has been selected to be edited;
command 2) [P] enters the powder menu;
command 3) [P] moves from the powder to the phase edit submenu;
command 4) [m 2] selects the second phase to have the magnetic flag changed;
command 5) [c] sets the phase to be magnetic-only;
command 6) [x x x x] returns to the main menu. Note that 4 "x" characters
are not needed in the final command, but extra characters are ignored.

EXPEDT prompts the user to supply a one-letter command, where
inputting a blank line provides further information on what the options
are (as demonstrated below). Note that commands can be combined onto
the same line (usually) and can
in many cases be spread over more than one line.

The input to and output from EXPEDT are shown below. User-typed
input is emphasized by display in this font:
Input

One more X command could now be entered to exit EXPEDT, but since the next
step will continue in EXPEDT, this is not necessary.
Note that the magnetic symmetry menu (as shown below) must be entered,
even if no changes will be made, for
GENLES to function once a magnetic phase has been added.

Setup Magnetic Symmetry and Moments

In the previous step, phase 2 was flagged as magnetic, but before a
magnetic scattering computation can be performed, the magnetic
symmetry needs to be set.
In this case, two operator colors must be
changed to change the space group from
Fmmm to Fmm'm'.
Once the magnetic symmetry is established,
the magnetic moments for each magnetic atom are supplied.

In EXPEDT, use the following commands:

L A

P 2

M

S

c 2

c 3

x

m 1 3.5

m 2 -3.5

m 3 -3.5

m 4 3.5

x

L

x x x x

Note that if EXPGUI were to be started at this point, the first command
would be "Y" to indicate that the correct file has been selected to be edited.
Command 1) [L] enters the least-squares menu and then [A]
moves from the least-squares to the atoms edit submenu;
command 2) [P 2] selects the second phase
command 3) [M] moves to the magnetism editing submenu;
command 4) [S] enters the spin-flip sub menu;
command 5) [C 2] toggles the color of the second symmetry operation (m perpendicular to y);
command 6) [C 3] toggles the color of the third symmetry operation (m perpendicular to z);
command 7) [x] returns to magnetism menu
command 8-11) [m N M] sets the magnetic moment for atom N to M Bohr magnetrons.
Note that in this case, these atoms are constrained by symmetry
to have only one magnetic moment, in the x direction.
If lower symmetry were present, components in other directions would be required.
Command 12) [x] returns to the atoms edit menu;
command 13) [L] lists the atoms in the current phase (#2)
-- this command is optional;
command 14) [x x x x] returns to the main menu.

The input to and output from EXPEDT are shown below. User-typed
input is emphasized by display in this font:
Input

Check Magnetic Form Factor

For this example, GSAS already has the correct magnetic form factor
loaded for atom type FE+3, but it is always a good idea to check this.
In some cases, the magnetic form factor for a problem will need to be loaded.
Many magnetic form factors can be found in the International Tables
of Crystallography, Volume C in section 4.4.5. Note that
GSAS uses the terms A1, B1, A2, B2, A3, B3, and C for the terms labeled
A, a, B, b, C, c and D in the International Tables.
GSAS terms A4 and B4 are not used in the International Tables and
should be specified as zero.

In EXPEDT, use the following commands:

L F M FE+3

C

.3972 13.244 .6295 4.903 -.0313 .35 0 0 .0044

N

U

x x x x

Note that if EXPGUI were to be started at this point, the first command
would be "Y" to indicate that the correct file has been selected to be edited.
Command 1) [L] enters the least-squares menu;
[F] moves from the least-squares to the form factor submenu;
[M FE+3] opens editing of the magnetic form factor for
Fe3+
command 2) [C] specifies that the saved values will be changed, the values
[.3972 13.244 .6295 4.903 -.0313 .35 0 0 .0044] specify the new <j0>
coefficients.
command 4) [N] indicates that the <j2> terms will not be changed.
command 5) [U] specifies that the entered coefficients are to be saved.
If this U is not entered, the original values will not be changed and the
new values are ignored
-- use care to remember to enter this command.
Command 6) [x x x x] returns to the main menu.
The input to and output from EXPEDT are shown below. User-typed
input is emphasized by display in this font:
Input

Setup Cell Constraints

So that the unit cell for the two phases will not be treated as independent
variables, constraints are needed to force the two sets of unit cell parameters
to change together. Note that since the second phase has dimensions double
to that of the first, the shifts applied to the second phase should be double
that of the first. However, the actual parameters that GSAS refines are not
lattice parameters, but rather are the reciprocal metric tensor terms, where
the diagonal terms, RM11, RM22 & RM33, are equal to a*2,
b*2 and c*2. Since the ratio of
(a*N2):(a*M2) is 4:1,
we use this ratio for our shifts.
In EXPEDT, use the following commands:

L

O

L

K

I 1,RM11,4 2,RM11,1 (+blank line)

I 1,RM22,4 2,RM22,1 (+blank line)

I 1,RM33,4 2,RM33,1 (+blank line)

L

x x x x

x

Note that if EXPGUI were to be started at this point, the first command
would be "Y" to indicate that the correct file has been selected to be edited.
Command 1) [L] enters the least-squares menu;
command 2) [O] moves from the least-squares to the least-squares overall parameters submenu;
command 3) [L] moves to the lattice parameters controls submenu;
command 4) [K] enters the lattice constraints submenu;
command 5-7) [I 1,RMxx,4 2,RMxx,1] constrains the shifts to reciprocal lattice
tensor element RMxx to be a factor of four larger for shifts applied to
phase 1 compared to phase 2. Note a blank line is needed to terminate
input of each constraint.
Command 8) [L] lists the constraints that have been input (optional);
command 9) [x x x x] returns to the main menu;
command 10) [x] exits EXPEDT

The input to and output from EXPEDT are shown below. User-typed
input is emphasized by display in this font:
Input

After the EXPEDT window is closed
since EXPEDT has changed the
experiment file,
(unless the Autoload EXP option is set)
there is a prompt to load the information from this changed file: press
the "Load new" button to continue
(screen image).

Setup Atomic Constraints

The Fe2a & Fe2b atoms in the magnetic phase
should move in concert with the Fe4 atom in the nuclear phase, where
the shift on Fe2a will be 50% the shift on Fe4 and the shift on Fe2b will be
-50% of the shift on Fe4. This is done on the Constraints menu, by pressing the
"New Constraint" button to open the Edit Constraint window.
Press the "New Column" button twice to create a second and third constraints
subwindow. Select
Phase 1, Fe4, variable Z and multiplier 1.0 in one column,
Phase 2, Fe2a, variable Z and multiplier 0.5 in another column, and
Phase 2, Fe2b, variable Z and multiplier -0.5 in the remainined column
(screen image).
Then press the "Save" button to enter the new constraint.
(Note that multipliers have an arbitrary scale; multipliers of -2,-1,1 would
provide equivalent results.)

Likewise, the constraint on the Uiso for the Fe atoms is
expanded to include the Fe atoms
in the second phase. This is done by clicking on the first "edit" button
to amend the first constraint. On the Editing Constraint #1 window, press the
"New Column" button, select Phase 2 in the new column, select all atoms;
the Variable selection defaults to Uiso and the Multiplier value defaults to 1.0
(screen image).
Then press the "Save" button to enter the modified constraint
(screen image).

Constrain Phase Fractions

GSAS scale factors are proportional to the number of scatters present in the
unit cell. Since the unit cell of the magnetic phase is eight times larger
than that of the nuclear phase, the scattering from this phase will be over
counted. To prevent this (so that magnetic moments are scaled properly
with respect to the nuclear scattering), the phase fraction of the second phase
is lowered by the ratio of the unit cell volumes (1/8). This is done by
changing the Phase Fraction for Phase 2 on the Scaling panel
(screen image).
Make sure that the scale factor
is refined, but not either of the phase fractions.

Phase 2 Refinement Flags

Constraints have been established on the unit cell and the atomic
parameters of phase 2. It is important to set the refinement flag and damping
values to be
the same for constrained parameters. Since unit cell paremeters, Uiso values
and Fe4 z are refined in phase 1, the same must be done in phase 2.
On the phase panel, select phase 2, noting that EXPGUI now shows
that the phase is magnetic-only directly below the phase selection buttons.

Click on the "Refine Cell" checkbutton.

Also, turn on the
X and U flags, so that the z coordinates
of the Fe atoms and the Uiso values will follow the atoms in the
nuclear phase, by highlighting
all atoms and selecting the "X" and "U" checkbuttons
(screen image).

Note that the first two Fe atoms in the magnetic phase will not change
position regardless of the X flag, as they are on special positions with
no degrees of freedom.

Refine with Magnetic Phase

Since a new phase has been added to the refinement, it is
necessary to run POWPREF
(screen image).
and then GENLES
(screen image).
The fit improves from the previous chi2 value of approximately 21
to a new value of approximately
15, as the low-angle magnetic lines are now computed with more intensity,
as can now be seen in LIVEPLOT
(screen image).

Constrain and Refine Profile Constraints

From the previous LIVEPLOT result, it is clear that the profile is a major
source of differences between the observed and computed diffraction data.
While it is possible to have different ordering ranges for the nuclear and
magnetic ordering, in most cases, it is best to have the same
parameters, for both the nuclear and magnetic phases.

A quick check of the Profile panel shows that the profile termes are
the same for both phases because they are still at their default values,
having not been refined.
(screen image).
To constrain the profile terms to refine to be the same, select the
Constraints panel and the click on the lower Profile tab and then
press the "Add Constraint" button
(screen image).
This will open the New Profile Constraint window
(screen image).
Select GU, GV & GW to be constrained (none of the other terms need
to be refined); then press the "Continue" button.
In the next window, select both phases in the top part of the window
and press the "Save" button
(screen image).
This generates the constraints, which show up on the Constraint panel
(screen image).

Select the check buttons for GU, GV & GW in both phases
(screen image)
and then start GENLES
(screen image).
The fit improves from the previous chi2 value of approximately 15
to a new value of approximately
3.4. Running POWPREF and then GENLES again causes
chi2 to drop from 3.4 to 2.6 just due to the expansion
of the peak shape range from POWPREF.
Subsequent refinement cycles improves chi2 slightly, to 2.45
(screen image).

Constrain & Refine Magnetic Moment

In most magnetic refinements, one wishes to refine magnetic moments.
It should be noted that the Fe1a and Fe1b atoms are symmetry related,
as is the case for Fe2a and Fe2b.
One could consider treating the two Fe1 atoms as having
different moments from the two Fe2 atoms, but this makes little
chemical sense, since there is no reason to expect either site to
have an accumulation of off-valence Fe atoms. Further, due to the
pseudo-symmmetry of the cell, there are few reflections that distinguish
the two non-equivalent Fe scatterers. Thus, it is best
to treat all Fe atoms as having a single magnetic moment. EXPGUI
can be used to set up constraints on the magnetic moments,
by creating a new atom constraint on the Constraints panel, where a
shift multiplier of 1.0 is applied to MX of atoms 1 & 4 in phase 2
and a shift multiplier of -1.0 is applied to MX of atoms 2 & 3 in phase 2
(screen image).
Press the "Save" button and the constraint appears
(screen image).

Changing the refinement flag for the magnetic moments must currently be
done from EXPEDT, using the following commands:

The refinement is then started with GENLES. The magnetic moments shift only
slightly (as can be seen from the LSTVIEW output) and the chi2
value drops only slightly
(screen image).

Further Model Improvements

At this point the refinement has progressed significantly, but for publication
one might wish to obtain a slightly better fit. To do this, the number of
background parameters can be increased to the point where little improvement
is seen by adding more terms, say to around 12-14 terms. The profile can be
improved further by switching to profile type 2 or 3 and allowing the LX term
to refine (don't forget to add a profile constraint).
There is a minor impurity phase, BaFeO3, that can be
included (Pm3m, a=4.0875, Ba: 0,0,0; Fe 1/2,1/2,1/2; O 1/2,1/2,0).
Note that the
phase fraction for this phase can be refined, and later the unit cell,
but the Uiso should be fixed at a reasonable level, such as the default of
0.025. With these additions, the fit can be improved to a reasonable
chi2 = 1.9 and very good R(F2) = 0.046.